Exam 8: Torque and Angular Momentum

A 2.00 kg mass is located at (4.00 m,0.00 m,0.00 m)and a 4.00 kg mass is located at (0.00 m,3.00 m,0.00 m).If this system of masses rotated about the Z-axis perpendicular to the X-Y plane,then the moment of inertia of this system is

The moment of inertia of a rod being rotated about one end is 1/3 ML².What is the moment of inertia of a rod of length L and mass M being rotated about a point located 0.40 L?

A 55kg girl swings on a swing,whose seat is attached to the pivot by 2.5m long rigid rods (considered to be massless in this problem).As she swings,she rises to a maximum height such that the angle of the rods with respect to the vertical is 32 degrees.What is the average torque on the rods due to her weight,as she moves during one cycle of her swinging from the bottom of her swing path to the highest point?

A 10 kg solid cylinder (I = 1/2 MR²)with a radius of 30.0 cm is rotating about a vertical axis through its center.If the angular momentum is increasing at the rate of 25.0 kg m²/s,then what is the angular acceleration?

A 5.00 kg object has a moment of inertia of 1.20 kg m².What torque is needed to give the object an angular acceleration of 2.0 rad/s²?

A 75.0 kg ladder that is 3.00 m in length is placed against a wall at an angle theta.The center of gravity of the ladder is at a point 1.20 m from the base of the ladder.The coefficient of static friction at the base of the ladder is 0.800.There is no friction between the wall and the ladder.What is the minimum angle the ladder makes with the horizontal for the ladder not to slip and fall?

A 1.5m long dowel is pivoted about the end so that it is a pendulum of sorts - it can freely swing in a vertical plane.At the other end of the dowel is a brass weight having mass 1.5kg.(The center of the brass weight is 1.5m from the pivot point.When the rod is positioned in its swing such that its angle with the vertical is 22.5 degrees,what is the torque on the rod about the pivot due to the presence of the brass weight?

A mass m₁ is connected by a light string that passes over a pulley of mass M to a mass m₂ sliding on a frictionless horizontal surface as shown in the figure.There is no slippage between the string and the pulley.The pulley has a radius of 25.0 cm and a moment of inertia of 1/2 MR².If m₁ is 1.00 kg,m₂ is 2.00 kg,and M is 4.00 kg,then what is the acceleration of m₁?

A 6.00 kg mass is located at (2.00 m,2.00 m,2.00 m)and a 5.00 kg mass is located at (-1.0 m,3.00 m,-2.00 m).If this system of masses rotated about the Z-axis perpendicular to the X-Y plane,then the moment of inertia of this system is

A mass m₁ is connected by a light string that passes over a pulley of mass M to a mass m₂ as shown in the figure.Both masses move vertically and there is no slippage between the string and the pulley.The pulley has a radius of 30.0 cm and a moment of inertia of MR².If m₁ is 4.00 kg,m₂ is 3.00 kg and M is 6.00 kg,then what is the tension in the string that is attached to m₂?

A 100 kg solid spherical rock (I = 2/5 MR²)has a diameter of 50.0 cm.The rock is rolling down a hill with a velocity of 5.00 m/s.The total kinetic energy (angular + translational)of the rolling rock is

A mass m₁ is connected by a light string that passes over a pulley of mass M to a mass m₂ sliding on a frictionless horizontal surface as shown in the figure.There is no slippage between the string and the pulley.The pulley has a radius of 25 cm and a moment of inertia of 1/2 MR².If m₁ is 4.00 kg,m₂ is 2.00 kg,and M is 4.00 kg,then what is the acceleration of m₁?

A mass m₁ is connected by a light string that passes over a pulley of mass M to a mass m₂ sliding on a frictionless horizontal surface as shown in the figure.There is no slippage between the string and the pulley.The pulley has a radius of 25.0 cm and a moment of inertia of 1/2 MR².If m₁ is 1.00 kg,m₂ is 2.00 kg,and M is 4.00 kg,then what is the tension in the string attached to m₂?

A mass m₁ is connected by a light string that passes over a pulley of mass M to a mass m₂ as shown in the figure.Both masses move vertically and there is no slippage between the string and the pulley.The pulley has a radius of 30.0 cm and a moment of inertia of MR².If m₁ is 4.00 kg,m₂ is 3.00 kg and M is 6.00 kg,then what is the acceleration of the masses?

A torque of 2.00 N.m is applied to a 10.0 kg object to give it an angular acceleration.If the angular acceleration is 1.75 rad/s²,then the moment of inertia is

A 4.00 kg hollow sphere of radius 5.00 cm starts from rest and rolls without slipping down a 30.0 degree incline.The acceleration of the center of mass of the hollow sphere is

A mass m₁ is connected by a light string that passes over a pulley of mass M to a mass m₂ as shown in the figure.Both masses move vertically and there is no slippage between the string and the pulley.The pulley has a radius of 20.0 cm and a moment of inertia of 1/2 MR².If m₁ is 3.00 kg,m₂ is 6.00 kg and M is 4.00 kg,then what is the tension in the string that is attached to mass m₁?

A 20.0 cm wrench is used to generate a torque at a bolt.A force of 50 N is applied perpendicularly at the end of the wrench.The torque generated at the bolt is

A 1.5m long,0.75kg dowel is pivoted about the end so that it is a pendulum of sorts - it can freely swing in a vertical plane.At the other end of the dowel is a brass weight having mass 1.5kg.(The center of the brass weight is 1.5m from the pivot point.When the rod is positioned in its swing such that its angle with the vertical is 22.5 degrees,what is the net torque on the rod about the pivot?

A mass m₁ is connected by a light string that passes over a pulley of mass M to a mass m₂ sliding on a frictionless incline as shown in the figure.There is no slippage between the string and the pulley.The pulley has a radius of 25.0 cm and a moment of inertia of 1/2 MR².If m₁ is 2.00 kg,m₂ is 1.00 kg,M is 4.00 kg,and the angle is 60.0 degrees,then what is the acceleration of m₁?